Structural morphology and relaxation spectra of viscoelastic heterogeneous materials

We analytically derive the relaxation spectra of a two-phase isotropic material whose phases are isotropic Maxwell media, according to the classical and to the generalized self-consistent schemes. Whereas these spectra are continuous in both cases, they exhibit strong differences which can be associated with the different underlying morphology, either symmetrical (polycrystal-type) in the first case or asymmetrical (composite-type) in the second case. The treatment is extended to the (N+1)-phase model which allows us to deal with coated inclusions or with an interphase between the matrix and the inclusions: the interphase is shown to strongly modify the resultant spectrum. More general cases are then considered for different kinds of constitutive behaviour as well as for coated fibre reinforced composites. As a whole, the spectral analysis method appears to be an efficient tool for the investigation of the connection between structural morphology and the overall behaviour of viscoelastic heterogeneous materials.